Problem: Baby Ehab was toying around with arrays. He has an array a of length n. He defines an array to be good if there's no way to partition it into 2 subsequences such that the sum of the elements in the first is equal to the sum of the elements in the second. Now he wants to remove the minimum number of elements in a so that it becomes a good array. Can you help him?

A sequence b is a subsequence of an array a if b can be obtained from a by deleting some (possibly zero or all) elements. A partitioning of an array is a way to divide it into 2 subsequences such that every element belongs to exactly one subsequence, so you must use all the elements, and you can't share any elements.

Input

The first line contains an integer n (2 ≤ n ≤ 100) — the length of the array a.

The second line contains n integers a_1, a_2, …, a_{n} (1 ≤ a_i ≤ 2000) — the elements of the array a.

Output

The first line should contain the minimum number of elements you need to remove.

The second line should contain the indices of the elements you're removing, separated by spaces.

We can show that an answer always exists. If there are multiple solutions, you can print any.

Examples

Input


4
6 3 9 12


Output


1
2

Input


2
1 2


Output


0

Note

In the first example, you can partition the array into [6,9] and [3,12], so you must remove at least 1 element. Removing 3 is sufficient.

In the second example, the array is already good, so you don't need to remove any elements.

Solution (in JAVA):

Solution:

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.lang.reflect.Array;
import java.util.*;

public class experiment
{

    static int M = 1_000_000_007;
    static int INF = 1_000_000_000;
    static final FastScanner fs = new FastScanner();

    //variable
    static int N = 100005;
    public static void main(String[] args) throws IOException {

//            int n = fs.nextInt();
//            long[] arr = new long[n];
//            for(int i=0;i<n;i++) {
//                arr[i] = fs.nextLong();
//            }
//            long xor = 0;
//            long max = -1;
//            for(int i=0;i<n;i++) {
//                max = Math.max(max,arr[i]);
//            }
//            for(int i=0;i<n;i++) {
//                if(max == arr[i]) {
//                    arr[i] = 0;
//                    break;
//                }
//            }
//
//            for(int i=1;i<n;i++) {
//                if((arr[i] | arr[i-1]) == max) {
//                    System.out.println("YES");
//                    continue outer;
//                }
//            }
//            System.out.println("NO");
            int n = fs.nextInt();
            int[] arr =fs.arrayIn(n);
            if(!equalPartition(n,arr)) {
                System.out.println(0);
                return;
            }
            for(int i=0;i<n;i++) {
                int temp = arr[i];
                arr[i] = 0;
                if(!equalPartition(n,arr)) {
                    System.out.println(1+"\n"+(i+1));
                    break;
                }
                arr[i] = temp;
            }
    }

    //function
    static boolean equalPartition(int n, int[] arr) {

        int sum = 0;
        for(int i=0;i<n;i++) {
            sum += arr[i];
        }
        if(sum%2 == 1) {
            return false;
        }
        int k = sum/2;
        boolean[][]dp = new boolean[k+1][n+1];
        for(int i=0; i<=n; i++) dp[0][i] = true;
        for(int i=1;i<=k; i++) dp[i][0] = false;
        for(int i=1; i<=k; i++){
            for(int j=1; j<=n; j++) {
                if(arr[j-1]<=i)
                    dp[i][j] = dp[i-arr[j-1]][j-1] || dp[i][j-1];
                else dp[i][j] = dp[i][j-1];
            }
        }
        return dp[k][n];
    }
    static void premutation(int n, ArrayList<Integer> arr,boolean[] chosen) {
        if(arr.size() == n) {

        }else {
            for(int i=1; i<=n; i++) {
                if(chosen[i]) continue;
                arr.add(i);
                chosen[i] = true;
                premutation(n,arr,chosen);
                arr.remove(i);
                chosen[i] = false;
            }
        }
    }
    static boolean isPalindrome(char[] c) {
        int n = c.length;
        for(int i=0; i<n/2; i++) {
            if(c[i] != c[n-i-1]) return false;
        }
        return true;
    }
    // Template
    static long nCk(int n, int k) {
        return (modMult(fact(n),fastexp(modMult(fact(n-k),fact(k)),M-2)));
    }

    static long fact (long n) {

        long fact =1;
        for(int i=1; i<=n; i++) {
            fact = modMult(fact,i);
        }
        return fact%M;
    }

    static int modMult(long a,long b) {
        return (int) (a*b%M);
    }

    static long fastexp(long x, int y){
        if(y==1) return x;

        long ans = fastexp(x,y/2);
        if(y%2 == 0) return modMult(ans,ans);

        return modMult(ans,modMult(ans,x));
    }

    static final Random random = new Random();

    static void ruffleSort(int arr[])
    {
        int n = arr.length;
        for(int i=0; i<n; i++)
        {
            int j = random.nextInt(n),temp = arr[j];
            arr[j] = arr[i];
            arr[i] = temp;
        }
        Arrays.sort(arr);
    }


    public static class Pairs implements Comparable<Pairs>
    {
        int value,index;
        Pairs(int value, int index) {
            this.value = value;
            this.index = index;
        }
        public int compareTo(Pairs p) {
            return Integer.compare(this.value,p.value);
        }
    }
}
class FastScanner
{
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer str = new StringTokenizer("");

    String next() throws IOException
    {
        while(!str.hasMoreTokens())
            str = new StringTokenizer(br.readLine());

        return str.nextToken();
    }

    char nextChar() throws IOException {
        return next().charAt(0);
    }

    int nextInt() throws IOException
    {
        return Integer.parseInt(next());
    }

    float nextfloat() throws IOException
    {
        return Float.parseFloat(next());
    }

    double nextDouble() throws IOException
    {
        return Double.parseDouble(next());
    }
    long nextLong() throws IOException
    {
        return Long.parseLong(next());
    }
    byte nextByte() throws IOException
    {
        return Byte.parseByte(next());
    }
    int [] arrayIn(int n) throws IOException
    {
        int  arr[] = new int[n];
        for(int i=0; i<n; i++)
        {
            arr[i] = nextInt();
        }
        return arr;
    }
}